What is the polar form of Vm sin (ωt + θ)?

What is the polar form of Vm sin (ωt + θ)?

• A. Vm + jθ
• B. Vm ∠ θ
• C. Vm cos(θ)
• D. Vm θ

Answer: (B)

The polar form of a sinusoidal function like Vm sin(ωt + θ) is represented as a magnitude and a phase angle. In this case, Vm represents the amplitude of the sinusoidal function, and the angle θ indicates the phase shift. When converting to polar form, the function is expressed as a complex number that captures both the magnitude and the phase information. Specifically, the sinusoidal function can be represented in the form of a complex exponential using Euler's formula, but for polar representation, we simply highlight the amplitude and the phase angle. Here, Vm is the peak value, and θ is the phase angle, making the representation Vm ∠ θ appropriate. This notation indicates that the sinusoidal function has an amplitude of Vm and is phased by θ degrees or radians. The polar form gives clear information about how the sinusoidal wave behaves in terms of its maximum output and the point in its cycle at t = 0. This understanding aligns with many applications in electrical engineering, where AC signals are commonly represented in polar form, particularly when analyzing phasors and their relationships.

The polar form of a sinusoidal function like Vm sin(ωt + θ) is represented as a magnitude and a phase angle. In this case, Vm represents the amplitude of the sinusoidal function, and the angle θ indicates the phase shift.

When converting to polar form, the function is expressed as a complex number that captures both the magnitude and the phase information. Specifically, the sinusoidal function can be represented in the form of a complex exponential using Euler's formula, but for polar representation, we simply highlight the amplitude and the phase angle.

Here, Vm is the peak value, and θ is the phase angle, making the representation Vm ∠ θ appropriate. This notation indicates that the sinusoidal function has an amplitude of Vm and is phased by θ degrees or radians. The polar form gives clear information about how the sinusoidal wave behaves in terms of its maximum output and the point in its cycle at t = 0.

This understanding aligns with many applications in electrical engineering, where AC signals are commonly represented in polar form, particularly when analyzing phasors and their relationships.